Question: $f(x) = 6x+5(h(x))$ $h(n) = 3n^{2}-6n$ $g(x) = -4x^{2}+2(h(x))$ $ g(f(2)) = {?} $
First, let's solve for the value of the inner function, $f(2)$ . Then we'll know what to plug into the outer function. $f(2) = (6)(2)+5(h(2))$ To solve for the value of $f$ , we need to solve for the value of $h(2)$ $h(2) = 3(2^{2})+(-6)(2)$ $h(2) = 0$ That means $f(2) = (6)(2)+(5)(0)$ $f(2) = 12$ Now we know that $f(2) = 12$ . Let's solve for $g(f(2))$ , which is $g(12)$ $g(12) = -4(12^{2})+2(h(12))$ To solve for the value of $g$ , we need to solve for the value of $h(12)$ $h(12) = 3(12^{2})+(-6)(12)$ $h(12) = 360$ That means $g(12) = -4(12^{2})+(2)(360)$ $g(12) = 144$